百度之星的一道与斐波那契数列有关的题
题目来源：http://astar.baidu.com/index.php?r=home/detail&id=2du熊对数学一直都非常感兴趣。最近在学习斐波那契数列的它，向你展示了一个数字串，它称之为“斐波那契”串：
11235813471123581347112358........
聪明的你当然一眼就看出了这个串是这么构造的：
1.先写下两位在0~9范围内的数字a, b，构成串ab；
2.取串最后的两位数字相加，将和写在串的最后面。
上面du熊向你展示的串就是取a = b = 1构造出来的串。
显然，步骤1之后不停地进行步骤2，数字串可以无限扩展。现在，du熊希望知道串的第n位是什么数字。 猜想,不管a,b是什么开始的,最终都构成一个周期重复性的数字串. 不是猜想,是必然的.
总共也就100种情况.可以用程序穷举验证.Flatten;
NestWhile[(xx[[#[[-2]] + 1, #[[-1]] + 1]] = 1; Join[#, IntegerDigits]]]) &, {i, j}, xx[[#[[-2]] + 1, #[[-1]] + 1]] == 0 &]}, {i, 0, 9}, {j, 0, 9}], 1]
{0,0} {0,0,0}
{0,1} {0,1,1,2,3,5,8,1,3,4,7,1,1}
{0,2} {0,2,2,4,6,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{0,3} {0,3,3,6,9,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{0,4} {0,4,4,8,1,2,3,5,8,1,3,4,7,1,1,2}
{0,5} {0,5,5,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{0,6} {0,6,6,1,2,3,5,8,1,3,4,7,1,1,2}
{0,7} {0,7,7,1,4,5,9,1,4}
{0,8} {0,8,8,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{0,9} {0,9,9,1,8,9,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{1,0} {1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{1,1} {1,1,2,3,5,8,1,3,4,7,1,1}
{1,2} {1,2,3,5,8,1,3,4,7,1,1,2}
{1,3} {1,3,4,7,1,1,2,3,5,8,1,3}
{1,4} {1,4,5,9,1,4}
{1,5} {1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{1,6} {1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{1,7} {1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{1,8} {1,8,9,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{1,9} {1,9,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{2,0} {2,0,2,2,4,6,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{2,1} {2,1,3,4,7,1,1,2,3,5,8,1,3}
{2,2} {2,2,4,6,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{2,3} {2,3,5,8,1,3,4,7,1,1,2,3}
{2,4} {2,4,6,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{2,5} {2,5,7,1,2,3,5,8,1,3,4,7,1,1,2}
{2,6} {2,6,8,1,4,5,9,1,4}
{2,7} {2,7,9,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{2,8} {2,8,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{2,9} {2,9,1,1,2,3,5,8,1,3,4,7,1,1}
{3,0} {3,0,3,3,6,9,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{3,1} {3,1,4,5,9,1,4}
{3,2} {3,2,5,7,1,2,3,5,8,1,3,4,7,1,1,2}
{3,3} {3,3,6,9,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{3,4} {3,4,7,1,1,2,3,5,8,1,3,4}
{3,5} {3,5,8,1,3,4,7,1,1,2,3,5}
{3,6} {3,6,9,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{3,7} {3,7,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{3,8} {3,8,1,1,2,3,5,8,1,3,4,7,1,1}
{3,9} {3,9,1,2,3,5,8,1,3,4,7,1,1,2}
{4,0} {4,0,4,4,8,1,2,3,5,8,1,3,4,7,1,1,2}
{4,1} {4,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{4,2} {4,2,6,8,1,4,5,9,1,4}
{4,3} {4,3,7,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{4,4} {4,4,8,1,2,3,5,8,1,3,4,7,1,1,2}
{4,5} {4,5,9,1,4,5}
{4,6} {4,6,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{4,7} {4,7,1,1,2,3,5,8,1,3,4,7}
{4,8} {4,8,1,2,3,5,8,1,3,4,7,1,1,2}
{4,9} {4,9,1,3,4,7,1,1,2,3,5,8,1,3}
{5,0} {5,0,5,5,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{5,1} {5,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{5,2} {5,2,7,9,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{5,3} {5,3,8,1,1,2,3,5,8,1,3,4,7,1,1}
{5,4} {5,4,9,1,3,4,7,1,1,2,3,5,8,1,3}
{5,5} {5,5,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{5,6} {5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{5,7} {5,7,1,2,3,5,8,1,3,4,7,1,1,2}
{5,8} {5,8,1,3,4,7,1,1,2,3,5,8}
{5,9} {5,9,1,4,5,9}
{6,0} {6,0,6,6,1,2,3,5,8,1,3,4,7,1,1,2}
{6,1} {6,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{6,2} {6,2,8,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{6,3} {6,3,9,1,2,3,5,8,1,3,4,7,1,1,2}
{6,4} {6,4,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{6,5} {6,5,1,1,2,3,5,8,1,3,4,7,1,1}
{6,6} {6,6,1,2,3,5,8,1,3,4,7,1,1,2}
{6,7} {6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{6,8} {6,8,1,4,5,9,1,4}
{6,9} {6,9,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{7,0} {7,0,7,7,1,4,5,9,1,4}
{7,1} {7,1,8,9,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{7,2} {7,2,9,1,1,2,3,5,8,1,3,4,7,1,1}
{7,3} {7,3,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{7,4} {7,4,1,1,2,3,5,8,1,3,4,7,1,1}
{7,5} {7,5,1,2,3,5,8,1,3,4,7,1,1,2}
{7,6} {7,6,1,3,4,7,1,1,2,3,5,8,1,3}
{7,7} {7,7,1,4,5,9,1,4}
{7,8} {7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{7,9} {7,9,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{8,0} {8,0,8,8,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{8,1} {8,1,9,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{8,2} {8,2,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{8,3} {8,3,1,1,2,3,5,8,1,3,4,7,1,1}
{8,4} {8,4,1,2,3,5,8,1,3,4,7,1,1,2}
{8,5} {8,5,1,3,4,7,1,1,2,3,5,8,1,3}
{8,6} {8,6,1,4,5,9,1,4}
{8,7} {8,7,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{8,8} {8,8,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{8,9} {8,9,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{9,0} {9,0,9,9,1,8,9,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{9,1} {9,1,1,0,1,1,2,3,5,8,1,3,4,7,1,1}
{9,2} {9,2,1,1,2,3,5,8,1,3,4,7,1,1}
{9,3} {9,3,1,2,3,5,8,1,3,4,7,1,1,2}
{9,4} {9,4,1,3,4,7,1,1,2,3,5,8,1,3}
{9,5} {9,5,1,4,5,9,1,4}
{9,6} {9,6,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{9,7} {9,7,1,6,7,1,3,4,7,1,1,2,3,5,8,1,3}
{9,8} {9,8,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
{9,9} {9,9,1,8,9,1,7,8,1,5,6,1,1,2,3,5,8,1,3,4,7,1,1}
不是猜想,是必然的.
总共也就100种情况.可以用程序穷举验证.Flatten;
NestWhile[(xx[[#[[-2]] + 1, #[[-1]] + 1]] = 1; Join[#, IntegerDigits]]]) &, {i, j}, xx[[#[[-2]] + 1, #[[-1]] +...
wayne 发表于 2012-12-13 21:17 http://bbs.emath.ac.cn/images/common/back.gif
厉害！再问个问题，用Join是不是比AppendTo更好呢 python用reduce(更像Fold)模仿Mathematica的Nest
intDigits=lambda n: map(int, str(n))
print reduce(lambda x,y: x+intDigits(sum(x[-2:])), range(10), )
AppendTo和Join的差别可以根据在文档中的路径看得出来
Mathematica > Core Language > Defining Variables and Functions > Assignments > AppendTo
Mathematica > Core Language > Expressions > Structural Operations on Expressions > Join
一个是属于赋值性质的,是要修改原值的, 一个是对结构的操作. 6# chyanog
:b:
我一定要抽个时间深入学一下Python,这语言挺不错的. 这个题目还真有些意思,matlab应该也能干这个活 其实也就是双重循环,然后再加上一个子函数